There are 35 connected vertex-transitive graphs on 17 vertices. The three that are self-complementary are shown here.
The order of the automorphism group is given in square brackets in each window's title.

Notation:

Cn means the cycle of length n

Cn(k) means the cycle of length n with chords of length k

~G means the complement of G

The suffix SC on a graph means self-complementary.

Paley(n) means the Paley graph on n vertices, where n is a prime power congruent to 1, (mod 4).
It has vertices 1,2,...,n,
and all edges [i,j] such that i-j is a perfect square in GF(n).
The Paley graphs are always self-complementary.